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Perturbation solution for solidification of pure metals on a sinusoidal mold surface

机译:用于在正弦模具表面上固化纯金属的摄动溶液

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摘要

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.
机译:线性摄动法用于解决二维热传导问题,在该问题中,液体通过热传递到有限厚度的正弦模具而凝固。有限差分法用于离散控制方程。熔融金属在开始凝固之前就完全润湿了模具表面,这导致了金属外壳厚度的相应起伏。研究了诸如壳和模具材料的热容量以及模具表面波长等物理参数对凝固壳厚度增长的影响。对于凝固壳和模具材料的扩散率无限大的极限情况,获得了分析结果,并将其与数值预测进行了比较,以建立模型和数值方法的有效性。

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